Isothermal Compressibilities

cf=−1V(∂V∂ρ)TThis equation is not rendering properly due to an incompatible browser. See Technical Requirements in the Orientation for a list of compatible browsers.

(18.15)

This expression can be also given in term of fluid density, as follows:

cf=−1ρ(∂ρ∂P)TThis equation is not rendering properly due to an incompatible browser. See Technical Requirements in the Orientation for a list of compatible browsers.

(18.16)

For liquids, the value of isothermal compressibility is very small because a unitary change in pressure causes a very small change in volume for a liquid. In fact, for slightly compressible liquid, the value of compressibility (co) is usually assumed independent of pressure. Therefore, for small ranges of pressure across which co is nearly constant, Equation (18.16) can be integrated to get:

co(p−pb)=ln(ρoρob)This equation is not rendering properly due to an incompatible browser. See Technical Requirements in the Orientation for a list of compatible browsers.

(18.17)

In such a case, the following expression can be derived to relate two different liquid densities (ρo, ρob)This equation is not rendering properly due to an incompatible browser. See Technical Requirements in the Orientation for a list of compatible browsers.
at two different pressures (p, pb):

ρo=ρob[1+co(p−pb)]This equation is not rendering properly due to an incompatible browser. See Technical Requirements in the Orientation for a list of compatible browsers.

(18.18)

The Vasquez-Beggs correlation is the most commonly used relationship for co.

For natural gases, isothermal compressibility varies significantly with pressure. By introducing the real gas law into Equation (18.16), it is easy to prove that, for gases:

cg=1P−1Z(∂Z∂P)rThis equation is not rendering properly due to an incompatible browser. See Technical Requirements in the Orientation for a list of compatible browsers.

(18.19)

Note that for an ideal gas, cg is just the reciprocal of the pressure. “cg” can be readily calculated by graphical means (chart of Z versus P) or by introducing an equation of state into Equation (18.19).

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